A large firm has established a system of deciding on annual pay increases for it

Question

A large firm has established a system of deciding on annual pay increases for its employees. The system is based on a series of evaluation scores determined by the supervisors of each employee. In the past, employees have received either 1) no pay increase; 2) a standard pay increase; or 3) a merit pay increase based on exceptional service. The proportion distribution of annual pay increase type was as follows: no pay increase was .20; standard increase was.60; merit increase was .20. The firm is concerned about the percentage of employees receiving no pay increase because it might indicate a lack of motivation. To potentially improve employee motivation, the firm developed a new evaluation system which was put into place for one year. After one year, the firm sampled its employee force to examine the distribution of pay increase type. The sample observations are below. You will perform the appropriate test to determine if the proportion distribution of pay increase type changed significantly after the new evaluation system was implemented. please show the work.

Category: Number of Employees

No pay increase                                                          75

Standard Pay Increase                                              360

Merit Pay Increase                                                    125

1. What is the appropriate NULL hypothesis for this problem?

2. What is the critical value for the decision rule for this problem using alpha=.05?

3. What is the value of the test statistic for this problem?

4. Write an appropriate conclusion for the test. Provide a brief post HOC analysis if you reject the HO.

Explanation / Answer

1. Null HYpothesis: H0 : THere is no significant chnge in pay increase system after the new avaluation system

ALternative Hypotheis : H1: THere is significanct change in pay increase system after the new evaluation system.

2. Here we will perform CHi- square test

560

Value of chi- square = (75 - 112)2/ 112 + ( 360 - 336)2/ 336 + (125 - 112)2/ 112 = 15.4464

Degree of Freedom = 2 here and for alpha = 0.05, critical value of chi-square = 5.991

Q3 Test statistic 2 = 15.4464

Q.4 so we can see that 2 > 2 critical so we can reject the null hypotheis can declare that there is significant difference after one year of new evaluation system effect on pay increase system.

560

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